Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(44.0774219157\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5520.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.24264 | −0.676182 | −0.338091 | − | 0.941113i | \(-0.609781\pi\) | ||||
−0.338091 | + | 0.941113i | \(0.609781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.41421 | −1.50163 | −0.750816 | − | 0.660511i | \(-0.770340\pi\) | ||||
−0.750816 | + | 0.660511i | \(0.770340\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.41421 | −1.07060 | −0.535302 | − | 0.844661i | \(-0.679802\pi\) | ||||
−0.535302 | + | 0.844661i | \(0.679802\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.07107 | 1.62221 | 0.811107 | − | 0.584898i | \(-0.198865\pi\) | ||||
0.811107 | + | 0.584898i | \(0.198865\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.24264 | 0.230753 | 0.115376 | − | 0.993322i | \(-0.463193\pi\) | ||||
0.115376 | + | 0.993322i | \(0.463193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6569 | 1.91403 | 0.957014 | − | 0.290043i | \(-0.0936695\pi\) | ||||
0.957014 | + | 0.290043i | \(0.0936695\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.24264 | 0.390394 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | −0.493197 | −0.246598 | − | 0.969118i | \(-0.579313\pi\) | ||||
−0.246598 | + | 0.969118i | \(0.579313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.41421 | 0.866968 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.58579 | −0.247658 | −0.123829 | − | 0.992304i | \(-0.539517\pi\) | ||||
−0.123829 | + | 0.992304i | \(0.539517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.41421 | −0.789744 | −0.394872 | − | 0.918736i | \(-0.629211\pi\) | ||||
−0.394872 | + | 0.918736i | \(0.629211\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.41421 | 0.618114 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.41421 | −0.881060 | −0.440530 | − | 0.897738i | \(-0.645209\pi\) | ||||
−0.440530 | + | 0.897738i | \(0.645209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.24264 | −0.302398 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.07107 | −0.936586 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.0711 | 1.57152 | 0.785760 | − | 0.618532i | \(-0.212272\pi\) | ||||
0.785760 | + | 0.618532i | \(0.212272\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.07107 | 0.137136 | 0.0685681 | − | 0.997646i | \(-0.478157\pi\) | ||||
0.0685681 | + | 0.997646i | \(0.478157\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.41421 | −0.671551 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.6569 | −1.30194 | −0.650971 | − | 0.759103i | \(-0.725638\pi\) | ||||
−0.650971 | + | 0.759103i | \(0.725638\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.07107 | −0.245791 | −0.122895 | − | 0.992420i | \(-0.539218\pi\) | ||||
−0.122895 | + | 0.992420i | \(0.539218\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.5563 | 1.82073 | 0.910366 | − | 0.413803i | \(-0.135800\pi\) | ||||
0.910366 | + | 0.413803i | \(0.135800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.24264 | −0.255573 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.65685 | −0.636446 | −0.318223 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318223 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −16.0711 | −1.76403 | −0.882014 | − | 0.471222i | \(-0.843813\pi\) | ||||
−0.882014 | + | 0.471222i | \(0.843813\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.41421 | −0.478789 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.24264 | −0.133225 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8284 | −1.14781 | −0.573905 | − | 0.818922i | \(-0.694572\pi\) | ||||
−0.573905 | + | 0.818922i | \(0.694572\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.41421 | −0.567564 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.6569 | −1.10506 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.07107 | 0.725476 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.17157 | −0.118955 | −0.0594776 | − | 0.998230i | \(-0.518943\pi\) | ||||
−0.0594776 | + | 0.998230i | \(0.518943\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.24264 | −0.225394 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.75736 | 0.274368 | 0.137184 | − | 0.990546i | \(-0.456195\pi\) | ||||
0.137184 | + | 0.990546i | \(0.456195\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.4853 | 1.03315 | 0.516573 | − | 0.856243i | \(-0.327208\pi\) | ||||
0.516573 | + | 0.856243i | \(0.327208\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | −0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.24264 | −0.313478 | −0.156739 | − | 0.987640i | \(-0.550098\pi\) | ||||
−0.156739 | + | 0.987640i | \(0.550098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.3848 | −1.76094 | −0.880471 | − | 0.474100i | \(-0.842774\pi\) | ||||
−0.880471 | + | 0.474100i | \(0.842774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.00000 | 0.284747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.757359 | −0.0712464 | −0.0356232 | − | 0.999365i | \(-0.511342\pi\) | ||||
−0.0356232 | + | 0.999365i | \(0.511342\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.41421 | −0.500544 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.41421 | −0.404650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.97056 | −0.542778 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.58579 | 0.142986 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.4142 | −1.01285 | −0.506424 | − | 0.862285i | \(-0.669033\pi\) | ||||
−0.506424 | + | 0.862285i | \(0.669033\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.00000 | 0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.65685 | −0.494242 | −0.247121 | − | 0.968985i | \(-0.579484\pi\) | ||||
−0.247121 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.07107 | 0.613139 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.485281 | −0.0414604 | −0.0207302 | − | 0.999785i | \(-0.506599\pi\) | ||||
−0.0207302 | + | 0.999785i | \(0.506599\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.51472 | −0.213296 | −0.106648 | − | 0.994297i | \(-0.534012\pi\) | ||||
−0.106648 | + | 0.994297i | \(0.534012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.41421 | 0.455959 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.1421 | 1.01538 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.24264 | 0.103196 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.00000 | 0.494872 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.5858 | −0.867221 | −0.433611 | − | 0.901100i | \(-0.642761\pi\) | ||||
−0.433611 | + | 0.901100i | \(0.642761\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.343146 | 0.0279248 | 0.0139624 | − | 0.999903i | \(-0.495555\pi\) | ||||
0.0139624 | + | 0.999903i | \(0.495555\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.41421 | −0.356868 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.6569 | 0.855979 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.48528 | 0.118538 | 0.0592692 | − | 0.998242i | \(-0.481123\pi\) | ||||
0.0592692 | + | 0.998242i | \(0.481123\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.41421 | 0.508680 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.65685 | −0.599731 | −0.299866 | − | 0.953981i | \(-0.596942\pi\) | ||||
−0.299866 | + | 0.953981i | \(0.596942\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.24264 | 0.174589 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0711 | 0.856705 | 0.428352 | − | 0.903612i | \(-0.359094\pi\) | ||||
0.428352 | + | 0.903612i | \(0.359094\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.3137 | 1.25490 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.07107 | 0.540738 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.3137 | −0.860165 | −0.430083 | − | 0.902790i | \(-0.641516\pi\) | ||||
−0.430083 | + | 0.902790i | \(0.641516\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12.0711 | −0.907317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.3431 | 0.922570 | 0.461285 | − | 0.887252i | \(-0.347389\pi\) | ||||
0.461285 | + | 0.887252i | \(0.347389\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.14214 | −0.456541 | −0.228271 | − | 0.973598i | \(-0.573307\pi\) | ||||
−0.228271 | + | 0.973598i | \(0.573307\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.07107 | −0.0791756 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | −0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.89949 | 0.723923 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.8995 | 1.00573 | 0.502866 | − | 0.864364i | \(-0.332279\pi\) | ||||
0.502866 | + | 0.864364i | \(0.332279\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.51472 | 0.540921 | 0.270461 | − | 0.962731i | \(-0.412824\pi\) | ||||
0.270461 | + | 0.962731i | \(0.412824\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.41421 | 0.387720 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.7990 | 0.983137 | 0.491569 | − | 0.870839i | \(-0.336424\pi\) | ||||
0.491569 | + | 0.870839i | \(0.336424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.4558 | −1.66274 | −0.831370 | − | 0.555719i | \(-0.812443\pi\) | ||||
−0.831370 | + | 0.555719i | \(0.812443\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.6569 | 0.751677 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.24264 | 0.0872163 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.58579 | −0.110756 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.8579 | −1.09691 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1716 | −0.700240 | −0.350120 | − | 0.936705i | \(-0.613859\pi\) | ||||
−0.350120 | + | 0.936705i | \(0.613859\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.07107 | 0.141907 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.00000 | −0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.6569 | 0.723434 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.5563 | −1.05120 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.8995 | 1.60765 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.9706 | 1.80608 | 0.903041 | − | 0.429554i | \(-0.141329\pi\) | ||||
0.903041 | + | 0.429554i | \(0.141329\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0000 | −1.32745 | −0.663723 | − | 0.747978i | \(-0.731025\pi\) | ||||
−0.663723 | + | 0.747978i | \(0.731025\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.82843 | 0.451235 | 0.225618 | − | 0.974216i | \(-0.427560\pi\) | ||||
0.225618 | + | 0.974216i | \(0.427560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.24264 | 0.147555 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.3431 | −1.20170 | −0.600850 | − | 0.799362i | \(-0.705171\pi\) | ||||
−0.600850 | + | 0.799362i | \(0.705171\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.41421 | −0.353184 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 5.65685 | 0.367452 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.07107 | 0.392705 | 0.196352 | − | 0.980533i | \(-0.437090\pi\) | ||||
0.196352 | + | 0.980533i | \(0.437090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.75736 | 0.242033 | 0.121016 | − | 0.992651i | \(-0.461385\pi\) | ||||
0.121016 | + | 0.992651i | \(0.461385\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.00000 | −0.383326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −38.2843 | −2.43597 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 16.0711 | 1.01846 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.34315 | −0.274137 | −0.137068 | − | 0.990562i | \(-0.543768\pi\) | ||||
−0.137068 | + | 0.990562i | \(0.543768\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.24264 | −0.140994 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.41421 | 0.276429 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.7279 | −0.793946 | −0.396973 | − | 0.917830i | \(-0.629939\pi\) | ||||
−0.396973 | + | 0.917830i | \(0.629939\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.00000 | −0.186411 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.24264 | 0.0769175 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.7279 | −1.83310 | −0.916551 | − | 0.399918i | \(-0.869039\pi\) | ||||
−0.916551 | + | 0.399918i | \(0.869039\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.41421 | −0.394022 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.8284 | 0.662689 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.4142 | −1.12273 | −0.561367 | − | 0.827567i | \(-0.689724\pi\) | ||||
−0.561367 | + | 0.827567i | \(0.689724\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.9706 | −1.45611 | −0.728054 | − | 0.685520i | \(-0.759575\pi\) | ||||
−0.728054 | + | 0.685520i | \(0.759575\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.41421 | 0.327683 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.24264 | −0.135236 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.6569 | −0.700392 | −0.350196 | − | 0.936676i | \(-0.613885\pi\) | ||||
−0.350196 | + | 0.936676i | \(0.613885\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.6569 | 0.638009 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.07107 | 0.541135 | 0.270567 | − | 0.962701i | \(-0.412789\pi\) | ||||
0.270567 | + | 0.962701i | \(0.412789\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 24.4558 | 1.45375 | 0.726875 | − | 0.686770i | \(-0.240972\pi\) | ||||
0.726875 | + | 0.686770i | \(0.240972\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −7.07107 | −0.418854 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.58579 | −0.0936060 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.48528 | 0.146193 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.17157 | 0.0686788 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −33.0416 | −1.93031 | −0.965156 | − | 0.261674i | \(-0.915725\pi\) | ||||
−0.965156 | + | 0.261674i | \(0.915725\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0711 | 0.702805 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.24264 | 0.130131 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.41421 | −0.313112 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | −0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.75736 | −0.158406 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.07107 | 0.0613292 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3848 | 1.27757 | 0.638783 | − | 0.769387i | \(-0.279438\pi\) | ||||
0.638783 | + | 0.769387i | \(0.279438\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.4853 | −0.596487 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.9706 | 1.18913 | 0.594566 | − | 0.804047i | \(-0.297324\pi\) | ||||
0.594566 | + | 0.804047i | \(0.297324\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0000 | 1.07394 | 0.536972 | − | 0.843600i | \(-0.319568\pi\) | ||||
0.536972 | + | 0.843600i | \(0.319568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00000 | 0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.55635 | 0.199744 | 0.0998722 | − | 0.995000i | \(-0.468157\pi\) | ||||
0.0998722 | + | 0.995000i | \(0.468157\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.78680 | −0.156031 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.24264 | 0.180987 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −31.2132 | −1.73675 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.41421 | −0.300327 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18.3848 | 1.01668 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.41421 | −0.298495 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.7990 | −1.69287 | −0.846433 | − | 0.532496i | \(-0.821254\pi\) | ||||
−0.846433 | + | 0.532496i | \(0.821254\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | −0.164399 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.6569 | −0.582246 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.65685 | 0.417095 | 0.208548 | − | 0.978012i | \(-0.433126\pi\) | ||||
0.208548 | + | 0.978012i | \(0.433126\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.757359 | 0.0411341 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.8995 | −1.29423 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.00000 | −0.0538382 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.1716 | −0.707087 | −0.353544 | − | 0.935418i | \(-0.615023\pi\) | ||||
−0.353544 | + | 0.935418i | \(0.615023\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8284 | −0.633161 | −0.316581 | − | 0.948566i | \(-0.602535\pi\) | ||||
−0.316581 | + | 0.948566i | \(0.602535\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.41421 | 0.288989 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.7574 | −0.838680 | −0.419340 | − | 0.907829i | \(-0.637738\pi\) | ||||
−0.419340 | + | 0.907829i | \(0.637738\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.07107 | −0.109921 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.41421 | 0.233625 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.7574 | 0.620530 | 0.310265 | − | 0.950650i | \(-0.399582\pi\) | ||||
0.310265 | + | 0.950650i | \(0.399582\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31.0000 | 1.63158 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.97056 | 0.313373 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.5563 | 0.814257 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.1421 | 0.999211 | 0.499606 | − | 0.866253i | \(-0.333478\pi\) | ||||
0.499606 | + | 0.866253i | \(0.333478\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.58579 | −0.0825527 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.41421 | −0.333009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.9706 | −1.29293 | −0.646463 | − | 0.762945i | \(-0.723753\pi\) | ||||
−0.646463 | + | 0.762945i | \(0.723753\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.72792 | −0.346506 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6569 | 0.906972 | 0.453486 | − | 0.891263i | \(-0.350180\pi\) | ||||
0.453486 | + | 0.891263i | \(0.350180\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.4142 | 0.584768 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −26.0711 | −1.33217 | −0.666085 | − | 0.745876i | \(-0.732031\pi\) | ||||
−0.666085 | + | 0.745876i | \(0.732031\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.24264 | −0.114296 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.00000 | −0.101666 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −36.1421 | −1.83248 | −0.916240 | − | 0.400631i | \(-0.868791\pi\) | ||||
−0.916240 | + | 0.400631i | \(0.868791\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.41421 | −0.223236 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.65685 | 0.285351 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.65685 | −0.284627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.0000 | −0.803017 | −0.401508 | − | 0.915855i | \(-0.631514\pi\) | ||||
−0.401508 | + | 0.915855i | \(0.631514\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.07107 | −0.353996 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.4853 | −0.723360 | −0.361680 | − | 0.932302i | \(-0.617797\pi\) | ||||
−0.361680 | + | 0.932302i | \(0.617797\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −57.6985 | −2.87417 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.72792 | 0.333491 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −28.4558 | −1.40705 | −0.703525 | − | 0.710670i | \(-0.748392\pi\) | ||||
−0.703525 | + | 0.710670i | \(0.748392\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.485281 | 0.0239372 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0711 | 0.593978 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.0711 | −0.788898 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.51472 | 0.123146 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.3848 | −1.77751 | −0.888756 | − | 0.458380i | \(-0.848430\pi\) | ||||
−0.888756 | + | 0.458380i | \(0.848430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.8701 | 0.724722 | 0.362361 | − | 0.932038i | \(-0.381971\pi\) | ||||
0.362361 | + | 0.932038i | \(0.381971\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.41421 | −0.263248 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.41421 | −0.214121 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.07107 | 0.0518326 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.1421 | −0.586228 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.17157 | 0.249106 | 0.124553 | − | 0.992213i | \(-0.460250\pi\) | ||||
0.124553 | + | 0.992213i | \(0.460250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.1716 | 1.16161 | 0.580806 | − | 0.814042i | \(-0.302738\pi\) | ||||
0.580806 | + | 0.814042i | \(0.302738\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.24264 | −0.0595801 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.07107 | 0.338255 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.20101 | 0.105048 | 0.0525242 | − | 0.998620i | \(-0.483273\pi\) | ||||
0.0525242 | + | 0.998620i | \(0.483273\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.0711 | 0.716048 | 0.358024 | − | 0.933712i | \(-0.383451\pi\) | ||||
0.358024 | + | 0.933712i | \(0.383451\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.8284 | −0.513317 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.5858 | 0.500691 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.7279 | −1.49733 | −0.748667 | − | 0.662947i | \(-0.769306\pi\) | ||||
−0.748667 | + | 0.662947i | \(0.769306\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.55635 | 0.167462 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.343146 | −0.0161224 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.41421 | −0.253822 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0000 | 0.888783 | 0.444391 | − | 0.895833i | \(-0.353420\pi\) | ||||
0.444391 | + | 0.895833i | \(0.353420\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.41421 | 0.206038 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.4853 | 0.860945 | 0.430473 | − | 0.902604i | \(-0.358347\pi\) | ||||
0.430473 | + | 0.902604i | \(0.358347\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.0416 | −1.30321 | −0.651603 | − | 0.758561i | \(-0.725903\pi\) | ||||
−0.651603 | + | 0.758561i | \(0.725903\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −10.6569 | −0.494200 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.4142 | 0.481912 | 0.240956 | − | 0.970536i | \(-0.422539\pi\) | ||||
0.240956 | + | 0.970536i | \(0.422539\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.6569 | −0.492088 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.48528 | −0.0684382 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.48528 | 0.206233 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.07107 | 0.324443 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.41421 | −0.293687 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.89949 | 0.452319 | 0.226160 | − | 0.974090i | \(-0.427383\pi\) | ||||
0.226160 | + | 0.974090i | \(0.427383\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2426 | 0.740601 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | −0.0455016 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.17157 | −0.0531984 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.07107 | −0.229792 | −0.114896 | − | 0.993378i | \(-0.536653\pi\) | ||||
−0.114896 | + | 0.993378i | \(0.536653\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.65685 | 0.346255 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −24.8995 | −1.12370 | −0.561849 | − | 0.827240i | \(-0.689910\pi\) | ||||
−0.561849 | + | 0.827240i | \(0.689910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.48528 | −0.247045 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.24264 | −0.100799 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.07107 | −0.0929001 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.82843 | 0.439981 | 0.219990 | − | 0.975502i | \(-0.429397\pi\) | ||||
0.219990 | + | 0.975502i | \(0.429397\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.0711 | −0.494619 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.6985 | −1.10125 | −0.550626 | − | 0.834752i | \(-0.685611\pi\) | ||||
−0.550626 | + | 0.834752i | \(0.685611\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.75736 | 0.122701 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16.3137 | −0.724517 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.7990 | 0.700278 | 0.350139 | − | 0.936698i | \(-0.386134\pi\) | ||||
0.350139 | + | 0.936698i | \(0.386134\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.5563 | 0.688172 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.07107 | −0.312195 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.4853 | 0.462037 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.1421 | 0.534011 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.3137 | 0.496617 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.07107 | −0.222168 | −0.111084 | − | 0.993811i | \(-0.535432\pi\) | ||||
−0.111084 | + | 0.993811i | \(0.535432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.3431 | −1.32681 | −0.663407 | − | 0.748259i | \(-0.730890\pi\) | ||||
−0.663407 | + | 0.748259i | \(0.730890\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.00000 | −0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −47.0416 | −2.04917 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0711 | 0.523840 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.58579 | 0.371892 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.24264 | −0.140192 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.3431 | −0.532646 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.4558 | 0.579584 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.4853 | 1.91257 | 0.956286 | − | 0.292434i | \(-0.0944651\pi\) | ||||
0.956286 | + | 0.292434i | \(0.0944651\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.14214 | 0.263584 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.3848 | −0.787517 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.68629 | 0.371399 | 0.185700 | − | 0.982607i | \(-0.440545\pi\) | ||||
0.185700 | + | 0.982607i | \(0.440545\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.07107 | 0.0457121 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.78680 | 0.374330 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.65685 | −0.240554 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.00000 | 0.127343 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.5858 | 1.08410 | 0.542052 | − | 0.840345i | \(-0.317647\pi\) | ||||
0.542052 | + | 0.840345i | \(0.317647\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.8284 | 0.457994 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.89949 | −0.417957 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.24264 | 0.136661 | 0.0683305 | − | 0.997663i | \(-0.478233\pi\) | ||||
0.0683305 | + | 0.997663i | \(0.478233\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.757359 | −0.0318623 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.14214 | 0.173647 | 0.0868237 | − | 0.996224i | \(-0.472328\pi\) | ||||
0.0868237 | + | 0.996224i | \(0.472328\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.7279 | −1.28592 | −0.642962 | − | 0.765898i | \(-0.722295\pi\) | ||||
−0.642962 | + | 0.765898i | \(0.722295\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.8995 | −0.580660 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.9411 | −0.913421 | −0.456711 | − | 0.889615i | \(-0.650972\pi\) | ||||
−0.456711 | + | 0.889615i | \(0.650972\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.51472 | −0.312301 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.0711 | −0.666740 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.3848 | 0.595757 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.41421 | −0.223850 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0000 | −0.577842 | −0.288921 | − | 0.957353i | \(-0.593296\pi\) | ||||
−0.288921 | + | 0.957353i | \(0.593296\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 75.3553 | 3.10496 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.7990 | −0.567615 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −26.8701 | −1.10342 | −0.551711 | − | 0.834036i | \(-0.686025\pi\) | ||||
−0.551711 | + | 0.834036i | \(0.686025\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.41421 | −0.180965 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 23.4558 | 0.959984 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.48528 | 0.346699 | 0.173350 | − | 0.984860i | \(-0.444541\pi\) | ||||
0.173350 | + | 0.984860i | \(0.444541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.313708 | 0.0127964 | 0.00639822 | − | 0.999980i | \(-0.497963\pi\) | ||||
0.00639822 | + | 0.999980i | \(0.497963\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.6569 | −0.433981 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.97056 | −0.242738 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.0416 | 0.569932 | 0.284966 | − | 0.958538i | \(-0.408018\pi\) | ||||
0.284966 | + | 0.958538i | \(0.408018\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.24264 | −0.0503543 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 29.3137 | 1.18591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 48.6274 | 1.96404 | 0.982021 | − | 0.188769i | \(-0.0604499\pi\) | ||||
0.982021 | + | 0.188769i | \(0.0604499\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.58579 | 0.0639451 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.8995 | 1.16345 | 0.581725 | − | 0.813386i | \(-0.302378\pi\) | ||||
0.581725 | + | 0.813386i | \(0.302378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.8284 | −0.433832 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.8579 | 0.633302 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.2426 | 0.528019 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.8995 | 1.26990 | 0.634949 | − | 0.772554i | \(-0.281021\pi\) | ||||
0.634949 | + | 0.772554i | \(0.281021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10.1716 | 0.404284 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −11.4142 | −0.452959 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.4853 | 1.28711 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.07107 | −0.0819302 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.0711 | −0.832257 | −0.416129 | − | 0.909306i | \(-0.636613\pi\) | ||||
−0.416129 | + | 0.909306i | \(0.636613\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.8284 | −1.25519 | −0.627595 | − | 0.778540i | \(-0.715961\pi\) | ||||
−0.627595 | + | 0.778540i | \(0.715961\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.00000 | 0.0787499 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.7279 | 1.67981 | 0.839904 | − | 0.542735i | \(-0.182611\pi\) | ||||
0.839904 | + | 0.542735i | \(0.182611\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.0711 | −1.06263 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.6569 | −0.417675 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 49.8406 | 1.95041 | 0.975207 | − | 0.221294i | \(-0.0710281\pi\) | ||||
0.975207 | + | 0.221294i | \(0.0710281\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.65685 | −0.221032 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.5563 | 0.606911 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.6985 | 1.39062 | 0.695308 | − | 0.718712i | \(-0.255268\pi\) | ||||
0.695308 | + | 0.718712i | \(0.255268\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4853 | 0.718994 | 0.359497 | − | 0.933146i | \(-0.382948\pi\) | ||||
0.359497 | + | 0.933146i | \(0.382948\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −23.8995 | −0.928179 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.07107 | 0.274204 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.24264 | 0.0481152 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −26.9706 | −1.04274 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.40202 | −0.0927290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.8701 | 1.26705 | 0.633524 | − | 0.773723i | \(-0.281608\pi\) | ||||
0.633524 | + | 0.773723i | \(0.281608\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.89949 | −0.342035 | −0.171018 | − | 0.985268i | \(-0.554706\pi\) | ||||
−0.171018 | + | 0.985268i | \(0.554706\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.17157 | −0.0449608 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0000 | 0.766402 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −44.7279 | −1.71147 | −0.855733 | − | 0.517417i | \(-0.826893\pi\) | ||||
−0.855733 | + | 0.517417i | \(0.826893\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.485281 | −0.0185416 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.82843 | −0.260521 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.7279 | 1.32303 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.627417 | 0.0238681 | 0.0119340 | − | 0.999929i | \(-0.496201\pi\) | ||||
0.0119340 | + | 0.999929i | \(0.496201\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.24264 | −0.0851909 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.51472 | −0.0953887 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.00000 | 0.265144 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.3431 | 0.693801 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.6985 | −1.12170 | −0.560848 | − | 0.827919i | \(-0.689525\pi\) | ||||
−0.560848 | + | 0.827919i | \(0.689525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −21.2132 | −0.800071 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.41421 | 0.203911 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.75736 | 0.103701 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.0711 | 1.39223 | 0.696117 | − | 0.717929i | \(-0.254910\pi\) | ||||
0.696117 | + | 0.717929i | \(0.254910\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.65685 | −0.212149 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.6569 | 0.399102 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.1421 | 0.454090 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.07107 | −0.226728 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.414214 | −0.0154476 | −0.00772378 | − | 0.999970i | \(-0.502459\pi\) | ||||
−0.00772378 | + | 0.999970i | \(0.502459\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4853 | 0.390492 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.75736 | −0.139738 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.24264 | 0.0461505 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.14214 | 0.339063 | 0.169532 | − | 0.985525i | \(-0.445775\pi\) | ||||
0.169532 | + | 0.985525i | \(0.445775\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.82843 | 0.326531 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −24.1716 | −0.892797 | −0.446399 | − | 0.894834i | \(-0.647294\pi\) | ||||
−0.446399 | + | 0.894834i | \(0.647294\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.00000 | 0.221313 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 23.8995 | 0.880349 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.14214 | 0.115585 | 0.0577927 | − | 0.998329i | \(-0.481594\pi\) | ||||
0.0577927 | + | 0.998329i | \(0.481594\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 38.2843 | 1.40641 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26.6274 | 0.976865 | 0.488433 | − | 0.872602i | \(-0.337569\pi\) | ||||
0.488433 | + | 0.872602i | \(0.337569\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5858 | −0.387833 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.0711 | −0.588010 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.24264 | −0.118484 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 36.7279 | 1.34022 | 0.670110 | − | 0.742261i | \(-0.266247\pi\) | ||||
0.670110 | + | 0.742261i | \(0.266247\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.34315 | 0.158273 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.343146 | 0.0124884 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −47.0000 | −1.70824 | −0.854122 | − | 0.520073i | \(-0.825905\pi\) | ||||
−0.854122 | + | 0.520073i | \(0.825905\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.24264 | 0.0814027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.1005 | −0.402393 | −0.201196 | − | 0.979551i | \(-0.564483\pi\) | ||||
−0.201196 | + | 0.979551i | \(0.564483\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.3848 | −0.665574 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.41421 | −0.159596 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −65.3553 | −2.35984 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.5858 | −0.598099 | −0.299049 | − | 0.954238i | \(-0.596670\pi\) | ||||
−0.299049 | + | 0.954238i | \(0.596670\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.7279 | 0.458385 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.1127 | −1.33485 | −0.667425 | − | 0.744677i | \(-0.732604\pi\) | ||||
−0.667425 | + | 0.744677i | \(0.732604\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.6569 | 0.382806 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.00000 | 0.107624 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.2132 | −0.401755 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.64466 | 0.166199 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.24264 | −0.0444084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.48528 | 0.0530120 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −45.7696 | −1.63151 | −0.815754 | − | 0.578399i | \(-0.803678\pi\) | ||||
−0.815754 | + | 0.578399i | \(0.803678\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.7279 | 1.05834 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.757359 | −0.0269286 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.79899 | −0.205928 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.41421 | 0.227489 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.5269 | −0.975053 | −0.487527 | − | 0.873108i | \(-0.662101\pi\) | ||||
−0.487527 | + | 0.873108i | \(0.662101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.8995 | 0.845503 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.8284 | −0.382604 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.8873 | −1.23115 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00000 | 0.0352454 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.4142 | 0.648211 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.58579 | 0.196386 | 0.0981929 | − | 0.995167i | \(-0.468694\pi\) | ||||
0.0981929 | + | 0.995167i | \(0.468694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.1716 | 0.848779 | 0.424389 | − | 0.905480i | \(-0.360489\pi\) | ||||
0.424389 | + | 0.905480i | \(0.360489\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.9706 | 0.840684 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.65685 | −0.268208 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.1421 | −0.494771 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.41421 | −0.189188 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.1127 | 1.36504 | 0.682521 | − | 0.730866i | \(-0.260883\pi\) | ||||
0.682521 | + | 0.730866i | \(0.260883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.6274 | 1.34647 | 0.673234 | − | 0.739430i | \(-0.264905\pi\) | ||||
0.673234 | + | 0.739430i | \(0.264905\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.24264 | 0.0780787 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.0416 | 1.07942 | 0.539712 | − | 0.841850i | \(-0.318533\pi\) | ||||
0.539712 | + | 0.841850i | \(0.318533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.20101 | −0.0417128 | −0.0208564 | − | 0.999782i | \(-0.506639\pi\) | ||||
−0.0208564 | + | 0.999782i | \(0.506639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.6569 | 0.404372 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.4853 | 0.917661 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.0711 | 0.383130 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.6569 | −0.368355 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.3431 | 1.39280 | 0.696400 | − | 0.717654i | \(-0.254784\pi\) | ||||
0.696400 | + | 0.717654i | \(0.254784\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4558 | −0.946753 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.07107 | −0.312424 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16.3137 | 0.561209 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.97056 | −0.205151 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −24.4558 | −0.839322 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00000 | −0.102839 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.48528 | −0.222052 | −0.111026 | − | 0.993818i | \(-0.535414\pi\) | ||||
−0.111026 | + | 0.993818i | \(0.535414\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.07107 | 0.241825 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.3431 | −0.694909 | −0.347454 | − | 0.937697i | \(-0.612954\pi\) | ||||
−0.347454 | + | 0.937697i | \(0.612954\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.4558 | −1.17562 | −0.587809 | − | 0.809000i | \(-0.700009\pi\) | ||||
−0.587809 | + | 0.809000i | \(0.700009\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.58579 | 0.0540435 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.85786 | 0.267485 | 0.133742 | − | 0.991016i | \(-0.457301\pi\) | ||||
0.133742 | + | 0.991016i | \(0.457301\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3137 | −0.384678 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.48528 | −0.0844046 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.6863 | 0.430353 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 57.6985 | 1.95504 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.17157 | −0.0396517 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.8284 | 0.433185 | 0.216593 | − | 0.976262i | \(-0.430506\pi\) | ||||
0.216593 | + | 0.976262i | \(0.430506\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.0416 | 1.11447 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.4142 | 0.856227 | 0.428113 | − | 0.903725i | \(-0.359178\pi\) | ||||
0.428113 | + | 0.903725i | \(0.359178\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.3848 | −0.551392 | −0.275696 | − | 0.961245i | \(-0.588908\pi\) | ||||
−0.275696 | + | 0.961245i | \(0.588908\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0711 | −0.405765 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.48528 | −0.0834476 | −0.0417238 | − | 0.999129i | \(-0.513285\pi\) | ||||
−0.0417238 | + | 0.999129i | \(0.513285\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.4142 | −0.382820 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.24264 | −0.0751313 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −38.2843 | −1.28113 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.3431 | 0.412586 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.41421 | 0.180775 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.2426 | 0.441667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.3137 | 0.943266 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.00000 | 0.0665558 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.14214 | −0.204171 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.97056 | −0.0654315 | −0.0327157 | − | 0.999465i | \(-0.510416\pi\) | ||||
−0.0327157 | + | 0.999465i | \(0.510416\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.75736 | 0.0914558 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.97056 | −0.164682 | −0.0823410 | − | 0.996604i | \(-0.526240\pi\) | ||||
−0.0823410 | + | 0.996604i | \(0.526240\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 36.0416 | 1.19280 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.07107 | −0.0354084 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.65685 | −0.186806 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −29.9411 | −0.987667 | −0.493833 | − | 0.869557i | \(-0.664405\pi\) | ||||
−0.493833 | + | 0.869557i | \(0.664405\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.3848 | −0.737603 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.2132 | 0.369087 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.00000 | −0.0986394 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.4853 | 0.344382 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.6152 | −0.676364 | −0.338182 | − | 0.941081i | \(-0.609812\pi\) | ||||
−0.338182 | + | 0.941081i | \(0.609812\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.4264 | −1.39047 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.9706 | −0.686545 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.89949 | 0.323748 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.1716 | 1.47569 | 0.737845 | − | 0.674970i | \(-0.235843\pi\) | ||||
0.737845 | + | 0.674970i | \(0.235843\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.0000 | −0.620042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.5563 | 1.15910 | 0.579552 | − | 0.814935i | \(-0.303228\pi\) | ||||
0.579552 | + | 0.814935i | \(0.303228\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.58579 | −0.0516403 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.00000 | −0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.45584 | 0.0473086 | 0.0236543 | − | 0.999720i | \(-0.492470\pi\) | ||||
0.0236543 | + | 0.999720i | \(0.492470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −84.2254 | −2.73407 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.55635 | −0.115323 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −57.3137 | −1.85657 | −0.928287 | − | 0.371866i | \(-0.878718\pi\) | ||||
−0.928287 | + | 0.371866i | \(0.878718\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.8995 | 0.449777 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.78680 | 0.0900843 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.485281 | −0.0156706 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.5685 | 2.66350 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.24264 | −0.104493 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.51472 | 0.241907 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.5269 | 1.11031 | 0.555155 | − | 0.831747i | \(-0.312659\pi\) | ||||
0.555155 | + | 0.831747i | \(0.312659\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.2132 | 1.00271 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −53.4558 | −1.71548 | −0.857740 | − | 0.514084i | \(-0.828132\pi\) | ||||
−0.857740 | + | 0.514084i | \(0.828132\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.51472 | −0.0806182 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.41421 | 0.173394 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.6985 | 1.30206 | 0.651030 | − | 0.759052i | \(-0.274337\pi\) | ||||
0.651030 | + | 0.759052i | \(0.274337\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.2843 | 0.776129 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.3848 | −0.586981 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.757359 | −0.0241560 | −0.0120780 | − | 0.999927i | \(-0.503845\pi\) | ||||
−0.0120780 | + | 0.999927i | \(0.503845\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.7990 | 0.439672 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.41421 | 0.172336 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.00000 | −0.0635963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.1716 | 0.767835 | 0.383918 | − | 0.923367i | \(-0.374575\pi\) | ||||
0.383918 | + | 0.923367i | \(0.374575\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 30.7990 | 0.977376 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.4558 | −0.743600 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.0833 | −1.26945 | −0.634725 | − | 0.772738i | \(-0.718887\pi\) | ||||
−0.634725 | + | 0.772738i | \(0.718887\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.00000 | 0.0949158 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5520.2.a.bk.1.1 | 2 | ||
4.3 | odd | 2 | 2760.2.a.q.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 8280.2.a.y.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.q.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
5520.2.a.bk.1.1 | 2 | 1.1 | even | 1 | trivial | ||
8280.2.a.y.1.1 | 2 | 12.11 | even | 2 |